{"title":"Laplace Expansion for Bartlett--Nanda--Pillai Test Statistic and Its Error Bound","authors":"H. Wakaki, V. V. Ulyanov","doi":"10.1137/s0040585x97t991635","DOIUrl":null,"url":null,"abstract":"Theory of Probability &Its Applications, Volume 68, Issue 4, Page 570-581, February 2024. <br/> We construct asymptotic expansions for the distribution function of the Bartlett--Nanda--Pillai statistic under the condition that the null linear hypothesis is valid in a multivariate linear model. Computable estimates of the accuracy of approximation are obtained via the Laplace approximation method, which is generalized to integrals for matrix-valued functions.","PeriodicalId":51193,"journal":{"name":"Theory of Probability and its Applications","volume":"96 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2024-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theory of Probability and its Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/s0040585x97t991635","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
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Abstract
Theory of Probability &Its Applications, Volume 68, Issue 4, Page 570-581, February 2024. We construct asymptotic expansions for the distribution function of the Bartlett--Nanda--Pillai statistic under the condition that the null linear hypothesis is valid in a multivariate linear model. Computable estimates of the accuracy of approximation are obtained via the Laplace approximation method, which is generalized to integrals for matrix-valued functions.
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Theory of Probability and Its Applications (TVP) accepts original articles and communications on the theory of probability, general problems of mathematical statistics, and applications of the theory of probability to natural science and technology. Articles of the latter type will be accepted only if the mathematical methods applied are essentially new.
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